Abstract
We study the behavior of neutral meson properties in the presence of a static uniform external magnetic field in the context of nonlocal chiral quark models. The formalism is worked out introducing Ritus transforms of Dirac fields, which allow to obtain closed analytical expressions for $\pi^0$ and $\sigma$ meson masses and for the $\pi^0$ decay constant. Numerical results for these observables are quoted for various parameterizations. In particular, the behavior of the $\pi^0$ meson mass with the magnetic field is found to be in good agreement with lattice QCD results. It is also seen that the Goldberger-Treiman and Gell-Mann-Oakes-Renner chiral relations remain valid within these models in the presence of the external magnetic field.
Highlights
The study of the behavior of strongly interacting matter under intense external magnetic fields has gained increasing interest in the last few years, especially due to its applications to the analysis of relativistic heavy ion collisions [1] and the description of compact objects like magnetars [2]
From the theoretical point of view, addressing this subject requires to deal with quantum chromodynamics (QCD) in nonperturbative regimes, present analyses are based either in the predictions of effective models or in the results obtained through lattice QCD (LQCD) calculations
It is seen that these curves turn out to be in good quantitative agreement with the results obtained from LQCD calculations
Summary
The study of the behavior of strongly interacting matter under intense external magnetic fields has gained increasing interest in the last few years, especially due to its applications to the analysis of relativistic heavy ion collisions [1] and the description of compact objects like magnetars [2]. In this work we focus on the effect of an intense external magnetic field on π0 and σ meson properties This issue has been studied in the last years following various theoretical approaches for lowenergy QCD, such as Nambu-Jona-Lasinio (NJL)-like models [3–8], chiral perturbation theory (ChPT) [9,10] and path integral Hamiltonians (PIH) [11,12]. Nonlocality arises naturally in the context of successful descriptions of lowenergy quark dynamics [16,17], and it has been shown [18] that nonlocal models can lead to a momentum dependence in quark propagators that is consistent with LQCD results In this framework it is possible to obtain an adequate description of the properties of light mesons at both zero and finite temperature [18–28].
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